Theory algebras of relations

Abstract

By (schematic) relation we mean a generalization of two other relation concepts: the n-ary or ordinary relations from mathematics and the partial tables from database theory. A theory algebra is similar to a boolean algebra. But next to this "semantical" order structure it also comprises a "syntactical" structure, which is more or less a boolean algebra as well.
This text introduces these kind of relations, a couple of operations on them and investigates their properties. Certain classes of relations together with this operations constitute these (powerful, flexible and elegant) theory algebras.
For the development of the whole theory some preliminary chapters are also covered: On generalizations of partial order structures and lattices, called quasi-hierarchies. On records, operations and order structures on records. On schemas and their various products. On graphs (here defined as record classes) and certain operations on them.